by Jim Muttram

The second half of the chessboard

I’ve just come across a very interesting concept in a podcast of Peter Day interviewing Erik Brynjolfsson and Andrew McAfee, the authors of The Race Against the Machine. They mentioned the famous legend about the origin of chess: When the inventor of the game showed it to the emperor of India, the emperor was so impressed by the new game, that he said to the man: “Name your reward.” The man responded that he was a humble man with simple wishes: “Give me one grain of rice for the first square of the chessboard, two grains for the next square, four for the next, eight for the next and so on for all 64 squares, with each square having double the number of grains as the square before.” The emperor agreed, amazed that the man had asked for such a small reward – or so he thought. After a week, his treasurer came back and informed him that the reward would add up to an astronomical sum, far greater than all the rice that could conceivably be produced in many many centuries. In fact, according to Wikipedia, the total number of grains would equal 18,446,744,073,709,551,615, which is “a much higher number than most people intuitively expect”.Brynjolfsson and McAfee point out that the effect in the second half of the chessboard is much more dramatic than the first: in the 32nd square the amount of rice is still relatively manageable. But after that each square doubles an already large number and quickly this outstrips human intuition. Brynjolfsson and McAfee say this same effect is happening with technology. Moore’s Law says technology power will double every 18 months or so and the effect of this again gets very much more significant “in the second half of the chessboard”. They calculate that we’ve had around 32 “squares” of exponential growth in technology and that now the 18 month advances are very much more dramatic than previously and this effect will increase dramatically (dramatic squared, if you like!). This is the reason behind the really quite remarkable advances in computing and robotics which is having the effect described in their book. “How the Digital Revolution is Accelerating Innovation, Driving Productivity, and Irreversibly Transforming Employment and the Economy”, as the subtitle puts it.